Alkali diffusion and electrical conductivity in sodium borate glasses

Journal of Non-Crystailine Solids 30 (1979) 241-252 © North-Holland Publishing Company

A L K A L I DIFFUSION AND ELECTRICAL CONDUCTIVITY IN SODIUM BORATE GLASSES * Y.H. HAN, N.J. K R E I D L and D.E. DAY ** Ceramic Engineering Department and Graduate Center for Materials Research, University of Missouri-Rolla, Rolla, MO 65401, USA Received 11 May 1978 Revised 24 August 1978

The diffusion coefficient of sodium, 22Na, and silver, 1lOAg ' and electrical conductivity for sodium borate glasses (4-24 mol% Na20) has been measured from 100°C to slightly below the glass transition temperature, Tg. Unlike silicate glasses where the self-diffusion coefficient, is much larger than the impurity diffusion coefficient, DNa and DAg had close to the same magnitude in the sodium borate glasses. In some glasses, DAg was slightly larger than DNa. NazOAg2O-B2 O3 glasses show a relatively small mixed alkali effect, despite the significant mass difference between Ag(-108) and Na(~23). It is concluded that the mixed alkali effect is more dependent upon the difference in ionic radii rather than differences in mass.

1. Introduction

Alkali ion m o t i o n in glass is important because of its fundamental relation to properties such as electrical conductivity, chemical durability and ion exchange kinetics. Previous work has concentrated on binary silicate glasses, and there is relatively little data for borate glasses. Below the glass transformation temperature (Tg) the electrical conductivity and alkali diffusion coefficients (DNa) are much lower in N a 2 0 - B 2 0 3 glasses [1] than in N a 2 0 - S i O 2 glasses [ 2 - 8 ] but the reasons for this are not known. Borate glasses [9] also exhibit smaller internal friction peaks than those found in alkali silicate glasses. The present work was undertaken to study the diffusion of Na ÷ and Ag* and the electrical conductivity in binary N a 2 0 - B 2 0 3 glasses. The behavior o f Ag ÷ impurity diffusion has been emphasized since silver, which is present mostly as Ag ÷, has been reported to behave similarly to sodium and other alkali ions in borate glasses [10]. A g 2 0 - N a 2 0 - B 2 0 3 glasses exhibit a mixed alkali internal friction peak [11] as well as a small minimum in electrical conductivity [12] as Ag,20 replace Na20. * Based on an M.S. thesis submitted by Y.H. Han, University of Missouri-Rolla, 1978. ** The authors gratefully acknowledge the f'mancial support of the National Science Foundation, Grant NSF-DMR-75-13348. 241

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Y.H. Han et al. /Alkali diffusion and electrical conductivity

Many theories have been proposed to explain the mixed alkali effect in glass. Some emphasize the structural features of the glass network, while oihers emphasize differences in the bonding and coordination environment of the alkali ions. The theories of Weyl [13] and Hendrickson and Bray [14] emphasize the differences in alkali ion mass which are considered to affect alkali ion oscillation in their local fields. Silver and sodium borate glasses are promising systems for testing this hypothesis. The glass network structures should be comparable, and Ag ÷ and Na ÷ have essentially the same size, but their mass differs by nearly a factor of five. In the present work, the diffusion coefficients of Na ÷ and Ag ÷ were measured in borate glasses containing from 4 to 24 mol% Na20 since Ag20 is readily soluble in borate glasses as opposed to its extremely low solubility in silicate glasses. Furthermore, the diffusion of Ag ÷ has practical relevance to photochromic glasses. Diffusion and electrical conductivity measurements provide an opportunity to compare alkali ion mobility in borate glasses with that in comparable silicate glasses.

2. Experimental 2.1. Glass preparation

The glasses listed in table 1 were prepared from reagent grade Na2CO3 and HaBO3, melted in a Pt crucible in an electric furnace open to t h e atmosphere for 6 h at 1000°C and then bubbled with dry 02 for 24 h at 1000°C to minimize the dissolved water (OH) content. The melt was poured into preheated molds, forming bars 1.2 × 1.2 × 8.0 cm which were then annealed in a furnace containing dry O2. Samples about 1.2 × 1.2 × 0.8 cm were cut from the bars, polished with 400-grit paper, reannealed simultaneously, and stored in mineral oil.

Table 1 Composition, density, and Tg temperature of sodium borate glasses Glass No.

Molar Composition (mole %) Na20 B203

Density (g cm -3)

Tg (°C) a) -+5°C

I II III IV V

4 8 12 16 24

1.92 2.01 2.08 2.13 2.25

260 285 325 365 425

a) Ref. [26,27].

96 92 88 84 76

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243

2.2. Diffusion measurements

The radioactive isotopes, 22Na and 11°Ag, were in the form of 22NaC1 and 1l°AgNO3 aqueous solutions. The diffusion coefficients reported are the average of two samples processed simultaneously. After polishing one face of a sample with 600-grit paper, the isotope was evaporated onto this face in a vacuum evaporator. The samples were then sealed in evacuated glass vials and heat-treated at 250°C to 410°C (+-I°C) for 1 to 200 d. The outer surfaces of each sample were removed after heat-treatment to eliminate surface diffusion effects. Each surface, except the one containing the isotope, was painted with an acid resistant resin. The sample was then dried until the weight was constant. A hydrofluoric acid solution (0.1% HF) was used to dissolve successive parallel sections of 1 to 5/ira thickness to a total depth of 5 to 50/am. The thickness of each section was determined from the glass density, the cross-sectional area, and the weight of each individual section (weighed to +0.00005 g). The sample was rinsed with methanol to remove any particles adhering to the glass surface after sectioning. The activity of each section was measured with NaI(T1) well-type scintillation counter. For thin f'tlm diffusion, the activity is given by the equation: Ai = (Ao/x/'~-~) exp(-X~i /4Dt) ,

(1)

where A i is the activity at distance X i from the surface;X/, the distance o f / t h section from the original surface in cm; t, the diffusion time in (s); Ao, the initial activity of tracer deposited on the sample and D is the diffusion coefficient in cm 2 S -1

"

2.3. Electrical conductivity measurements

The dc and ac electrical conductivity was measured for glasses I to IV and glasses IV and V, respectively. In the ac measurements *, a sample with silver paste electrodes was placed between copper electrodes in an electric furnace containing dry 02. The conductivity was measured from 200°C to slightly below Tg of each glass. The results were extrapolated to zero frequency as an estimate of the dc conductivity. In the dc measurements **, a sample with gold electrodes was placed in an apparatus [15] designed for measuring thermally stimulated currents and then cooled to -163°C. An electrical field (~497 Vcm -l) was applied to the sample, and the current flowing in the sample measured as the sample was heated (0.05-0.12°C s -1) from -163°C to ~230°C. This procedure was repeated and the conductivity calcu* Using a Model B 224 universal bridge (Wayne Kerr Co., Ltd., Chessington, Surrey, England) coupled with an external oscillator, from 1 to 20 kHz. ** Using a Model 610B Electrometer (Keithley Instruments, Inc., Cleveland, Ohio, USA).

Y.H. Han et al. / A Ikali diffusion and electrical conductivity

244

lated from the applied field and measured current for the second heating. Over the temperature range from 95°C to 230°C, the conductivity (o) measured in this way obeyed the Arrhenius equation: (2)

o = Oo e x p ( - E o / R T ) ,

where Oo is the pre-exponential factor; Eo, the activation energy for ionic conduction;R, the gas constant and T the absolute temperature in K.

3. Results

3.1. Diffusion coefficients

The diffusion coefficients, Dna and DAg, were calculated from the slope ofln Ai versus X~i, eq. (1). Fig. 1 shows that DNa and Dag varied, within experimental error, according to the Arrhenius equation: (3)

D = Do e x p ( - E D / R T ) ,

where Do is the pre-exponential factor; ED, the activation energy for diffusion;R the gas constant and T the absolute temperature in K. The diffusion coefficients, activation energies, and pre-exponential factors given in table 2 were calculated from eq. (3) using a least squares analysis of the experimental data. It was impos-

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Table 3 Calculated sodium diffusion coefficients (D~a) and Haven ratio (fa) Glass

Temperature (°C)

DN a a) (cm 2 s -1)

a (ohm-1 cm-1)

D ~ a b) (cm 2 s-1 )

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III

320 285 250

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8.52 × 10 -1° 1.85 × 10 -1° 3.29 ×10 -11

7.34 × 10 -14 1.50 × 10 -14 2.50 × 10 - i s

0.25 0.25 0.26

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360 320 285 250

8.80 2.22 5.60 1.18

3.23 8.97 2.55 6.12

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360 320 285 250

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0.23 0.26 0.30 0.31

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× 10 -8 × 10 -9 × 10 -9 × 10 -1°

5 . 6 4 × 1 0 -6 1.86× 10 -6 6.13 X10 -7 1 . 7 4 × 1 0 -7

a) DN a determined from tracer measurements. b)Dl~ a calculated from conductivity (o). sible t o m e a s u r e d i f f u s i o n c o e f f i c i e n t s < 1 0 -16 c m 2 s -1 b y t h e t r a c e r d i f f u s i o n t e c h n i q u e . Because o f this, t h e DNa values for glasses I a n d II, t a b l e 2, were c a l c u l a t e d f r o m t h e electrical c o n d u c t i v i t y using t h e N e r n s t - E i n s t e i n e q u a t i o n :

D* = ( o k T / N e 2) f a ,

(4)

w h e r e D* is t h e d i f f u s i o n c o e f f i c i e n t ; a, t h e electrical c o n d u c t i v i t y ; k, is t h e Boltzm a n n c o n s t a n t ; e, t h e e l e c t r o n charge; N , t h e c o n c e n t r a t i o n o f charge carriers a n d f o = t h e H a v e n ratio. A H a v e n ratio o f 0.3 was a s s u m e d in t h e s e c a l c u l a t i o n s , since f o = 0.2 t o 0 . 4 was f o u n d for t h e o t h e r glasses w h e r e DNa c o u l d b e m e a s u r e d , t a b l e 3.

3.2. Electrical conductivity T h e t e m p e r a t u r e d e p e n d e n c e o f t h e electrical c o n d u c t i v i t y is s h o w n in fig. 2. T h e a c t i v a t i o n energies a n d p r e - e x p o n e n t i a l factors in t a b l e 4 were c a l c u l a t e d f r o m Table 4 Pre-exponential factor (oo) and activation energy (E o) for electrical conductivity Glass No.

ao (ohm -1 cm-1 )

E o (Kcal mo1-1 )

I II III IV V

1.76 21.6 29.5 4.46 85.9

30.3 31.7 28.6 25.5 20.8

-+ 1.3 ± 1.2 ± 0.6 ± 0.7 +- 1.6

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eq. (2) using a least squares analysis of the experimental data. As shown in fig. 2, the ac measurements were limited to conductivities > 1 0 -9 o h m -1 c m - 1 , but the data for glass IV show that the two methods are in excellent agreement.

4. Discussion 4.1. Activation energy

The compositional dependence of the activation energy for DNa , Dng and electrical conductivity shown in fig. 3 is very similar, reaching a maximum at ~8 tool% Na20 or Ag20. The present activation energy data for electrical conductivity in the sodium borate glasses agree well with previous results [12]. The decrease in activation energy with increasing Na20 concentration is similar to that observed in silicate glasses [2-5] except for the maximum at ~8 mol% Na20 or Ag20. This maximum in activation energy cannot be accounted for by the model proposed by Anderson and Stuart [16] where the activation energy for ionic conduction is considered to be the sum of the electrostatic and strain energy needed to move an ion from one site to another. In this model, the electrostatic energy decreases with increasing alkali content since the distance between alkali sites becomes smaller, whereas the strain energy increases with increasing alkali con-

Y.H. Han et al. / Alkali diffusion and electrical conductivity

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tent as the coordination number of boron changes from 3 to 4 and the network structure becomes more compact. The decrease in activation energy above 8 mol% Na20 agrees qualitatively with this model. Experimental values are ~2 Kcal mo1-1 greater than the calculated values. Below 8 mol% Na~O, however, the calculated values increase steeply, rather than decrease, with decreasing alkali content.

4.2. Comparison Of DNa ill borate and silicate glasses A comparison of DNa in borate and silicate glasses [5-8] of corresponding soda content is shown in fig. 4 where DNa has been plotted versus T/Tg because of the widely different Tg's for silicate and borate glasses. DNa in silicate glasses is obviously much larger than in borate glasses at any given fraction of Tg and, somewhat surprisingly, tends to be nearly independent of Na20 content. The electrical conductivity of silicate glasses [2-5] is also significantly greater than in borate glasses at any given fraction of Tg. This difference in DNa does not seem to be related to differences in Do, since the Do values in borate and silicate glasses are reasonably similar, fig. 5. Rather, it seems to be the consequence of the larger activation energy in borate glasses. The similar.

Y.H. Han et al. / A lkali diffusion and electrical conductivity

249

ity in the activation energy for He diffusion in borate [17] and silicate glasses [18] bottom curves in fig. 5, suggests that the strain energy for Na + diffusion is also similar in borate and silicate glasses; He and Na ÷ have nearly identical radii of 0.95 A and 0.98 A, respectively. Thus, the principal reason for the larger activation energy for Na ÷ diffusion in borate glasses is a stronger electrostatic interaction of the Na ÷ ions with the boron-oxygen network.

4.3. Mixed alkali effect Introducing a second alkali ion into silicate glasses typically leads to a significant reduction in the diffusion coefficient of the original alkali ion, [6], [19] and [20], fig. 6; Moreover, the alkali self-diffusion coefficient in single alkali silicate glasses has always been observed to be significantly larger than the impurity alkali ion dif-

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250

Y.H. Han et al. / Alkali diffusion and electrical conductivity

fusion coefficient such that at some composition a crossover (intersection) in the diffusion coefficients is observed, fig. 6. However, no significant difference between DNa and DAg was found in glasses III to V where DNa and DAg could be measured. Even though these glasses contain only Na20, DAg is slightly greater than DNa in glasses III and IV over the temperature range investigated, fig. 1. In glass V, DNa is slightly larger than DAg as usually found. The difference between DNa and DAg appears to be increasing with increasing Na20 content. Using the DNa and DAg values in Ag-borate [21] and in Na-borate glasses, the mixed alkali effect which has been associated with the crossover in alkali diffusion coefficients, can be interpreted in Na20-Ag20-B203 glasses as shown schematically in fig. 7. In 16 mol% glasses at 360°C, fig. 7a,DAg DNa in both sodium and silver borate glasses. The diffusion coefficients in fig. 7 are assumed linearly dependent upon the Na/(Ag + Na) ratio, but would most likely be curves as in fig. 6. This simplification does not affect the conclusion reached, however, that the crossover in diffusion coefficients which is commonly found in mixed alkali silicate glasses would probably not occur in fig. 7a. However, a crossover at lower temperatures is likely, figs. 7b and 7c, since DNa could be >DAg in the 16 mol% sodium borate glass, see fig. 1. These data suggest, therefore, that the deviation from additivity (i.e. mixed alkali effect) for properties dependent upon alkali ion mobility would not only be small, but would diminish with increasing temperature. Certain assumptions must be made in order to estimate how the magnitude of the mixed alkali effect varies with total Na20 or Ag20 content, since DNa values are only available for the 16 mol% Ag20-B203 glass. If it is assumed that the difference between DNa and DAg in a 24 tool% Ag-borate glass is approximately equal to that in the 16 mol% Ag-borate glass at any given temperature, figs. 7d-f, then the

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Y.H. Han et al. / Alkali diffusion and electrical conductivity

251

mixed alkali effect should be more pronounced in 24 mol% glasses than in 16 mol% glasses, but should again become smaller with increasing temperature. At temperatures close to Tg, it becomes likely that a crossover in DNa and DAg would be absent. The diffusion coefficient data lead to the conclusions, therefore, that in mixed Na-Ag borate glasses the mixed alkali effect for a property such as electrical conductivity would be both small and diminish with increasing temperature, but would become more pronounced with increasing total alkali content. These conclusions are in substantial agreement with the observed electrical conductivity of Na-Ag borate glasses [12] and dielectric loss [23] and mechanical damping [11,23] in other mixed alkali borate glasses. The conductivity isotherms for X Ag20 • (27.4 X) • Na:O • 72.6 B203 glasses [12] show only a small minimum at 100°C which is even less pronounced at 300°C and which occurs in the soda-rich compositions, Na/ (Ag + Na) ~0.8, in basic agreement with the expected crossover of DNa and DAg in fig. 7. There are no data for mixed Na-Ag borate glasses against which the compositional dependence can be compared, but in N a - K borate glasses [23] the minimum deviation from additivity in the dielectric loss and the magnitude of the mixed alkali internal friction peak both become larger with increasing total alkali content in agreement with what is expected from the diffusion coefficient data. Thus, those characteristics of the mixed alkali effect in N a - A g borate glasses which are known at this time can be empirically accounted for by the relative temperature and compositional dependence Of DNa and DAg. The most recent theory for the mixed alkali effect by Hendrickson and Bray [14] is based upon the mass difference of dissimilar alkali ions. Despite the large difference in mass between Ag(109) and Na(23), the magnitude of the mixed alkali effect in N a - A g borate glasses [11], [12] and [23] appears much smaller than in other mixed alkali silicates [6], [19] and [20] borate [23,24] or germanate [25] glasses where the mass difference is much less. Thus, the present results and those from other investigations of Na-Ag borate glasses indicate that the difference in alkali ion size may be more important to the mixed alkali effect than the difference in ion mass.

References [1] K.S. Evstropiev and A.O. Ivanov, in Proc. 6th Int. Congr. on Glass, Advances in Glass Technology Part 2, Washington, D.C., 1962 (Plenum Press, New York, 1963) pp. 79-85. [2] K. Otto and M.E. Milberg,J. Am. Ceram. Soc. 6 (1968) 326-329. [3] Y. Haven and B. Verkerk, Phys. Chem. Glasses2 (1965) 38-45. [4] R.M. Hakim and D.R. Uhlmann, Phys. Chem. Glasses5 (1971) 132-138. [5] C. Lim and D.E. Day, J. Am. Ceram. Soc. 5, 6 (1977) 198-203. [6] G.L. McVay and D.E. Day, J. Am. Ceram. Soc. 9 (1970) 508-513. [7] G.H. Frischat, Ionic Diffusion Oxide Glasses (Trans. Tech. Publications, Ohio, 1975) p. 138. [8] R. Terai, Phys. Chem. Glasses4 (1969) 146-152.

252 [9] [10] [11] [12] [13]

Y.H. Han et al. / Alkali diffusion and electrical conductivitY

H. Rotger, J. Am. Ceram. Soc. 2 (1958) 54-60. E.N. Boulos and N.J. Kreidl, J. Am. Ceram. Soc. 8 (1971) 368-375. E.N. Boulos and N.J. Kreidl, J. Am. Ceram. Soc. 6 (1971) 318-319. K. Matusita, M. Ito, K. Kamiya and S. Sakka, Yogo-Kyokai-Shii 10 (1976) 496-508. W.A. Weyl and E.C. Marboe, The Constitution of Glasses, Vol. II: Part 2 (lnterscience, New York, 1962) p. 925. [14] J.R. Hendrickson and P.J. Bray, Phys. Chem. Glasses 2 (1972) 43-49;4 (1972) 107-115. [15 ] C. Hong, M.S. Thesis, Univ. Of Mo.-Rolla, Rolla, Mo, 1975. [16] O.L. Anderson and D.A. Stuart, J. Am. Ceram. Soc. 12 (1954) 573-581. [17] J.E. Shelby, J. Appl. Phys. 9 (1973) 3880-3888. [18] J.E. Shelby, J. Am. Ceram. Soc. 5 (1973) 263-266. [19] J.W. Fleming and D.E. Day, J. Am. Ceram. Soc. 4 (1972) 186-192. [20] R. Hiyami and R. Terai, Phys. Chem. Glasses 4 (1972) 102-106. [21] Y. Kawamoto, Kobe University, Japan, private communication (1977). [22] D.E. Day, J. Non-Crystalline Solids 21 (1976) 343-372. [23] W.J. van Gemert, H.M. van Ass, J.M. Stevels, J. Non-Crystalline Solids 16 (1974) 281293. [24] K.A. Kostanyan, The Structure of Glass, Vol. 2 (Consultants Bureau, New York, 1960) pp. 234-236. [25] A.O. Ivanov, Soy. Phys. Solid St. 9 (1964) 1933-1937. [26] E. Jenckel, Z. Elektrochem. 4 (1935) 211-215. [27] R.R. Shaw and D.R. Uhlmann, J. Am. Ceram. Soc. 7 (1968) 377-382. [28] K.K. Evstropev and V.K. Pavlovskli,Consultants Bureau Transl. 3 (1967) 92-96.